Face Expressions from one mesh to another
If the meshes are different regarding their vertice (count and inter-vertice-connection - the "edges") there is no native way to do this - at least not with native blender tools. I don't know of any addon, which does this - I often need to have such a tool and didn't find any.

The reason is, that the shape keys are recordings of vertex displacements. 
Think of a sphere with shape keys and try to transfer them to a cube....
(ok...that example is extreme...;) )